Delay-decomposing approach to robust stability for switched interval networks with state-dependent switching

Area of Science:

• Control Systems Engineering
• Network Stability Analysis
• Nonlinear Systems Theory

Background:

• Nonlinear uncertain switched networks with discrete time-varying delays present significant control challenges.
• Existing methods for stability analysis often yield conservative results.

Purpose of the Study:

• To develop novel robust stability criteria for nonlinear uncertain switched networks with discrete time-varying delays.
• To reduce conservatism in stability analysis and improve upon existing results.

Main Methods:

• Utilizing the strictly complete property of matrices and a delay-decomposing approach.
• Designing a state-dependent switching rule based on a new Lyapunov-Krasovskii functional.
• Applying a piecewise delay method to analyze the Lyapunov functional across subintervals.

Main Results:

• Derivation of new delay-dependent robust stability criteria using linear matrix inequalities.
• Demonstration of significantly less conservative results compared to existing references.
• Validation of the theoretical findings through an illustrative example.

Conclusions:

• The proposed method effectively enhances the stability analysis of complex network systems.
• The derived criteria offer improved performance and reduced conservatism for nonlinear uncertain switched networks.
• This work contributes to the advancement of robust control theory for systems with time-varying delays.